They're not at all rare! That's a bit of a myth/assumption perpetuated by the idea that oily skin doesn't need moisturizer. However, I could go to the store right now and find a couple dozen moisturizers that won't make my oily skin worse.

For the most part, any moisturizer that doesn't feel heavy on your skin (and there are loads) will be a good start. I like Cerave Moisturizing Lotion (not the cream) because it has hyaluronic acid and ceramides. The hyaluronic acid is going to help plump up the skin by retaining water and the hyaluronic acid is moisturizing. It's unscented and super light weight, and readily available at the drug store.

In terms of getting rid of oily skin... You might not be able to. It depends on why your skin is oily. If it's just the way your body is then that's just something to accept. However, sometimes people experience excessive oily skin due to diet or very dehydrated skin. My oily skin improves a tiny bit when I clean up my diet and make sure my skin stays hydrated - but ultimately its still oily. You can try adding an oil to your skin routine st night (eg rose hip). Doing this will also help a bit with oily skin because your skin won't produce as much of its own.

It's hard to tell you what the one right thing is. For some, these things help immensely with oily skin while others only notice slight improvements.